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<h1 id="前言"><a href="#前言" class="headerlink" title="前言"></a>前言</h1><p>这是当初考离散时整理的笔记，其中包含了自己对于一些知识点的体悟。纸质笔记只有一份，不易分享。因此把它拍照整理后放到这里。这样既能帮助到更多被离散折磨的学弟学妹们🥺，又能当作纸质笔记的一个备份。</p>
<p>本文主要是助离散期末考试只求低分飘过的小可爱们一臂之力~ 如若对自己的成绩有更高的要求，那么本文能做的最多也只是帮助你回顾一下基础知识而已。</p>
<p>一般来说，离散考试的难度主要是在于题目所涉及的知识点数量太过繁杂，并不在于知识点会考多深。所以考前最重要的是了解每个知识的概念和简单运用，这样基本就能够通过考试。不过为了防止某次考试老师把许多题目难度都设定得很高，在看完本文后若是还有一些的复习时间，可以去做一做更难的题目。</p>
<hr>
<h1 id="一、数理逻辑"><a href="#一、数理逻辑" class="headerlink" title="一、数理逻辑"></a>一、数理逻辑</h1><h2 id="1-命题逻辑"><a href="#1-命题逻辑" class="headerlink" title="1. 命题逻辑"></a>1. 命题逻辑</h2><p><img src="https://img-blog.csdnimg.cn/20210402102711628.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h2 id="2-等值演算"><a href="#2-等值演算" class="headerlink" title="2. 等值演算"></a>2. 等值演算</h2><p><img src="https://img-blog.csdnimg.cn/20210402102912324.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h2 id="3-主合取范式、主析取范式"><a href="#3-主合取范式、主析取范式" class="headerlink" title="3. 主合取范式、主析取范式"></a>3. 主合取范式、主析取范式</h2><p><img src="https://img-blog.csdnimg.cn/20210402103222167.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"><img src="https://img-blog.csdnimg.cn/20210402103317734.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h2 id="4-【题】推理证明"><a href="#4-【题】推理证明" class="headerlink" title="4. 【题】推理证明"></a>4. 【题】推理证明</h2><p><img src="https://img-blog.csdnimg.cn/20210402103426676.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h2 id="5-辖域、自由变元、约束变元"><a href="#5-辖域、自由变元、约束变元" class="headerlink" title="5. 辖域、自由变元、约束变元"></a>5. 辖域、自由变元、约束变元</h2><p><img src="https://img-blog.csdnimg.cn/20210402103455230.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h1 id="二、集合"><a href="#二、集合" class="headerlink" title="二、集合"></a>二、集合</h1><h2 id="1-环和、环积，幂集，笛卡尔乘积"><a href="#1-环和、环积，幂集，笛卡尔乘积" class="headerlink" title="1. 环和、环积，幂集，笛卡尔乘积"></a>1. 环和、环积，幂集，笛卡尔乘积</h2><p><img src="https://img-blog.csdnimg.cn/20210402103544435.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h1 id="三、-二元关系"><a href="#三、-二元关系" class="headerlink" title="三、 二元关系"></a>三、 二元关系</h1><h2 id="1-自反、对称、传递"><a href="#1-自反、对称、传递" class="headerlink" title="1. 自反、对称、传递"></a>1. 自反、对称、传递</h2><p><img src="https://img-blog.csdnimg.cn/20210402103629338.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h2 id="2-amp-3-合成运算，逆关系、闭包"><a href="#2-amp-3-合成运算，逆关系、闭包" class="headerlink" title="2&amp;3. 合成运算，逆关系、闭包"></a>2&amp;3. 合成运算，逆关系、闭包</h2><p><img src="https://img-blog.csdnimg.cn/20210402103716392.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h2 id="4-哈斯图、上下界、偏序"><a href="#4-哈斯图、上下界、偏序" class="headerlink" title="4. 哈斯图、上下界、偏序"></a>4. 哈斯图、上下界、偏序</h2><p><img src="https://img-blog.csdnimg.cn/20210402103803288.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h2 id="5-等价关系、划分"><a href="#5-等价关系、划分" class="headerlink" title="5. 等价关系、划分"></a>5. 等价关系、划分</h2><p><img src="https://img-blog.csdnimg.cn/20210402103854995.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h1 id="四、代数"><a href="#四、代数" class="headerlink" title="四、代数"></a>四、代数</h1><h2 id="1-幺元（么元、单位元）、零元、逆元，半群、群、阿尔贝群、独异点、循环独异点"><a href="#1-幺元（么元、单位元）、零元、逆元，半群、群、阿尔贝群、独异点、循环独异点" class="headerlink" title="1. 幺元（么元、单位元）、零元、逆元，半群、群、阿尔贝群、独异点、循环独异点"></a>1. 幺元（么元、单位元）、零元、逆元，半群、群、阿尔贝群、独异点、循环独异点</h2><p><img src="https://img-blog.csdnimg.cn/20210402103921865.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"><img src="https://img-blog.csdnimg.cn/20210402103951340.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h2 id="2-【题】由表判断"><a href="#2-【题】由表判断" class="headerlink" title="2. 【题】由表判断"></a>2. 【题】由表判断</h2><p><img src="https://img-blog.csdnimg.cn/20210402104107333.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h2 id="3-【题】证明"><a href="#3-【题】证明" class="headerlink" title="3. 【题】证明"></a>3. 【题】证明</h2><p><img src="https://img-blog.csdnimg.cn/20210402104149894.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h1 id="五、图论"><a href="#五、图论" class="headerlink" title="五、图论"></a>五、图论</h1><h2 id="1-简单图、平凡图、多重图、子图、补图、出度、入度、同构"><a href="#1-简单图、平凡图、多重图、子图、补图、出度、入度、同构" class="headerlink" title="1. 简单图、平凡图、多重图、子图、补图、出度、入度、同构"></a>1. 简单图、平凡图、多重图、子图、补图、出度、入度、同构</h2><p><img src="https://img-blog.csdnimg.cn/20210402104253172.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h2 id="2-路径、回路、连通度、欧拉"><a href="#2-路径、回路、连通度、欧拉" class="headerlink" title="2. 路径、回路、连通度、欧拉"></a>2. 路径、回路、连通度、欧拉</h2><p><img src="https://img-blog.csdnimg.cn/20210402104320553.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
<hr>
<h2 id="3-矩阵表示、矩阵转置、欧拉公式"><a href="#3-矩阵表示、矩阵转置、欧拉公式" class="headerlink" title="3. 矩阵表示、矩阵转置、欧拉公式"></a>3. 矩阵表示、矩阵转置、欧拉公式</h2><p><img src="https://img-blog.csdnimg.cn/2021040210434713.jpg?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1NoZXJsb29vY2s=,size_16,color_FFFFFF,t_70#pic_center" alt="img"></p>
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fa-stream"></i><span>目录</span><span class="toc-percentage"></span></div><div class="toc-content"><ol class="toc"><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%89%8D%E8%A8%80"><span class="toc-text">前言</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E4%B8%80%E3%80%81%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91"><span class="toc-text">一、数理逻辑</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#1-%E5%91%BD%E9%A2%98%E9%80%BB%E8%BE%91"><span class="toc-text">1. 命题逻辑</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#2-%E7%AD%89%E5%80%BC%E6%BC%94%E7%AE%97"><span class="toc-text">2. 等值演算</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#3-%E4%B8%BB%E5%90%88%E5%8F%96%E8%8C%83%E5%BC%8F%E3%80%81%E4%B8%BB%E6%9E%90%E5%8F%96%E8%8C%83%E5%BC%8F"><span class="toc-text">3. 主合取范式、主析取范式</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#4-%E3%80%90%E9%A2%98%E3%80%91%E6%8E%A8%E7%90%86%E8%AF%81%E6%98%8E"><span class="toc-text">4. 【题】推理证明</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#5-%E8%BE%96%E5%9F%9F%E3%80%81%E8%87%AA%E7%94%B1%E5%8F%98%E5%85%83%E3%80%81%E7%BA%A6%E6%9D%9F%E5%8F%98%E5%85%83"><span class="toc-text">5. 辖域、自由变元、约束变元</span></a></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E4%BA%8C%E3%80%81%E9%9B%86%E5%90%88"><span class="toc-text">二、集合</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#1-%E7%8E%AF%E5%92%8C%E3%80%81%E7%8E%AF%E7%A7%AF%EF%BC%8C%E5%B9%82%E9%9B%86%EF%BC%8C%E7%AC%9B%E5%8D%A1%E5%B0%94%E4%B9%98%E7%A7%AF"><span class="toc-text">1. 环和、环积，幂集，笛卡尔乘积</span></a></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E4%B8%89%E3%80%81-%E4%BA%8C%E5%85%83%E5%85%B3%E7%B3%BB"><span class="toc-text">三、 二元关系</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#1-%E8%87%AA%E5%8F%8D%E3%80%81%E5%AF%B9%E7%A7%B0%E3%80%81%E4%BC%A0%E9%80%92"><span class="toc-text">1. 自反、对称、传递</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#2-amp-3-%E5%90%88%E6%88%90%E8%BF%90%E7%AE%97%EF%BC%8C%E9%80%86%E5%85%B3%E7%B3%BB%E3%80%81%E9%97%AD%E5%8C%85"><span class="toc-text">2&amp;3. 合成运算，逆关系、闭包</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#4-%E5%93%88%E6%96%AF%E5%9B%BE%E3%80%81%E4%B8%8A%E4%B8%8B%E7%95%8C%E3%80%81%E5%81%8F%E5%BA%8F"><span class="toc-text">4. 哈斯图、上下界、偏序</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#5-%E7%AD%89%E4%BB%B7%E5%85%B3%E7%B3%BB%E3%80%81%E5%88%92%E5%88%86"><span class="toc-text">5. 等价关系、划分</span></a></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%9B%9B%E3%80%81%E4%BB%A3%E6%95%B0"><span class="toc-text">四、代数</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#1-%E5%B9%BA%E5%85%83%EF%BC%88%E4%B9%88%E5%85%83%E3%80%81%E5%8D%95%E4%BD%8D%E5%85%83%EF%BC%89%E3%80%81%E9%9B%B6%E5%85%83%E3%80%81%E9%80%86%E5%85%83%EF%BC%8C%E5%8D%8A%E7%BE%A4%E3%80%81%E7%BE%A4%E3%80%81%E9%98%BF%E5%B0%94%E8%B4%9D%E7%BE%A4%E3%80%81%E7%8B%AC%E5%BC%82%E7%82%B9%E3%80%81%E5%BE%AA%E7%8E%AF%E7%8B%AC%E5%BC%82%E7%82%B9"><span class="toc-text">1. 幺元（么元、单位元）、零元、逆元，半群、群、阿尔贝群、独异点、循环独异点</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#2-%E3%80%90%E9%A2%98%E3%80%91%E7%94%B1%E8%A1%A8%E5%88%A4%E6%96%AD"><span class="toc-text">2. 【题】由表判断</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#3-%E3%80%90%E9%A2%98%E3%80%91%E8%AF%81%E6%98%8E"><span class="toc-text">3. 【题】证明</span></a></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E4%BA%94%E3%80%81%E5%9B%BE%E8%AE%BA"><span class="toc-text">五、图论</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#1-%E7%AE%80%E5%8D%95%E5%9B%BE%E3%80%81%E5%B9%B3%E5%87%A1%E5%9B%BE%E3%80%81%E5%A4%9A%E9%87%8D%E5%9B%BE%E3%80%81%E5%AD%90%E5%9B%BE%E3%80%81%E8%A1%A5%E5%9B%BE%E3%80%81%E5%87%BA%E5%BA%A6%E3%80%81%E5%85%A5%E5%BA%A6%E3%80%81%E5%90%8C%E6%9E%84"><span class="toc-text">1. 简单图、平凡图、多重图、子图、补图、出度、入度、同构</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#2-%E8%B7%AF%E5%BE%84%E3%80%81%E5%9B%9E%E8%B7%AF%E3%80%81%E8%BF%9E%E9%80%9A%E5%BA%A6%E3%80%81%E6%AC%A7%E6%8B%89"><span class="toc-text">2. 路径、回路、连通度、欧拉</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#3-%E7%9F%A9%E9%98%B5%E8%A1%A8%E7%A4%BA%E3%80%81%E7%9F%A9%E9%98%B5%E8%BD%AC%E7%BD%AE%E3%80%81%E6%AC%A7%E6%8B%89%E5%85%AC%E5%BC%8F"><span class="toc-text">3. 矩阵表示、矩阵转置、欧拉公式</span></a></li></ol></li></ol></div></div><div class="card-widget card-recent-post"><div class="item-headline"><i class="fas fa-history"></i><span>最新文章</span></div><div class="aside-list"><div class="aside-list-item"><a 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